In order to illustrate this discussion, we consider a phenomenologically
rich SI model, the SI-scotogenic model [1]},
where the SM is extended by one inert doublet scalar, \(S^{T}\equiv \Big (S^{\pm }\,,\,[S^{0}+iA^{0}]/\sqrt{2}\Big )\) ,
three singlet Majorana fermions \(N_{i}\) , and one real neutral singlet
scalar \(\phi \) . The model is assigned by a global \(Z_{2}\)  symmetry
\(\lbrace S,\,N_{i}\rbrace \rightarrow \lbrace -S,\,-N_{i}\rbrace \) , where all other fields
being \(Z_{2}\) -even. This global symmetry makes the lightest \(Z_{2}\) -odd
field \(N_{1}\)  as a stable DM candidate. One can easily construct
the effective potential (REF ) for this model by deriving
the field dependant masses through the relevant parts of the SI Lagrangian
density
\(-\mathcal {L}\supset & =\frac{1}{2}y_{i}\phi \overline{N_{i}^{c}}\,N_{i}+\frac{1}{6}\lambda _{h}(\left|\mathcal {H}\right|^{2})^{2}+\frac{\lambda _{\phi }}{24}\phi ^{2}+\frac{\lambda _{S}}{2}|S|^{4}+\frac{\omega _{1}}{2}|\mathcal {H}|^{2}\phi ^{2}+\frac{\omega _{2}}{2}\,\phi ^{2}|S|^{2}\nonumber \\& +\lambda _{3}\,|\mathcal {H}|^{2}|S|^{2}+\lambda _{4}\,|\mathcal {H}^{\dagger }S|^{2}+\lbrace \frac{\lambda _{5}}{2}(\mathcal {H}^{\dagger }S)^{2}+h.c.\rbrace ,\) 
